Solve by Addition/Elimination 2x-y=9 3x+4y=-14

$2 x - y = 9$ $3 x + 4 y = - 14$

Step 1

Multiply each equation by the value that makes the coefficients of $y$ opposite.

$(4) \cdot (2 x - y) = (4) (9)$

$3 x + 4 y = - 14$

Step 2

Simplify.

Simplify the left side.

Simplify $(4) \cdot (2 x - y)$ .

Apply the distributive property.

$4 (2 x) + 4 (- y) = (4) (9)$

$3 x + 4 y = - 14$

Multiply.

Multiply $2$ by $4$ .

$8 x + 4 (- y) = (4) (9)$

$3 x + 4 y = - 14$

Multiply $- 1$ by $4$ .

$8 x - 4 y = (4) (9)$

$3 x + 4 y = - 14$

$8 x - 4 y = (4) (9)$

$3 x + 4 y = - 14$

$8 x - 4 y = (4) (9)$

$3 x + 4 y = - 14$

$8 x - 4 y = (4) (9)$

$3 x + 4 y = - 14$

Simplify the right side.

Multiply $4$ by $9$ .

$8 x - 4 y = 36$

$3 x + 4 y = - 14$

$8 x - 4 y = 36$

$3 x + 4 y = - 14$

$8 x - 4 y = 36$

$3 x + 4 y = - 14$

Step 3

Add the two equations together to eliminate $y$ from the system.

		$8$	$x$	$-$	$4$	$y$	$=$		$3$	$6$
$+$		$3$	$x$	$+$	$4$	$y$	$=$	$-$	$1$	$4$
	$1$	$1$	$x$				$=$		$2$	$2$

Step 4

Divide each term in $11 x = 22$ by $11$ and simplify.

Divide each term in $11 x = 22$ by $11$ .

$\frac{11 x}{11} = \frac{22}{11}$

Simplify the left side.

Cancel the common factor of $11$ .

Cancel the common factor.

$\frac{11 x}{11} = \frac{22}{11}$

Divide $x$ by $1$ .

$x = \frac{22}{11}$

Simplify the right side.

Divide $22$ by $11$ .

$x = 2$

Step 5

Substitute the value found for $x$ into one of the original equations, then solve for $y$ .

Substitute the value found for $x$ into one of the original equations to solve for $y$ .

$8 (2) - 4 y = 36$

Multiply $8$ by $2$ .

$16 - 4 y = 36$

Move all terms not containing $y$ to the right side of the equation.

Subtract $16$ from both sides of the equation.

$- 4 y = 36 - 16$

Subtract $16$ from $36$ .

$- 4 y = 20$

Divide each term in $- 4 y = 20$ by $- 4$ and simplify.

Divide each term in $- 4 y = 20$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{20}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{20}{- 4}$

Divide $y$ by $1$ .

$y = \frac{20}{- 4}$

Simplify the right side.

Divide $20$ by $- 4$ .

$y = - 5$

Step 6

The solution to the independent system of equations can be represented as a point.

$(2, - 5)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(2, - 5)$

Equation Form:

$x = 2, y = - 5$

Step 8

Solve by Addition/Elimination 2x-y=9 3x+4y=-14

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